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Ibn Hamzah Al-Maghribi: Pioneer of Arithmetic and Algebra

Prof. Dr. Faid Mohammed Said

Abstract

Ibn Hamzah al-Maghribi was a pioneering figure in the field of mathematics within Islamic civilization, with notable contributions to the development of arithmetic and algebra. This study sheds light on his biography, scholarly environment, teachers and students, his most important works and accomplishments, as well as his influence on contemporary scholars and Orientalists, and his lasting impact on modern mathematics and academic education.

Introduction

Islamic civilization played a decisive role in the development of mathematical and geometrical sciences. Among the scholars who laid the foundations of algebra was Ibn Hamzah al-Maghribi, regarded as a pioneer in the fields of arithmetic and algebra. His works served as references for both Muslim and European scholars, especially after their translation into Latin during the Renaissance.

Biography

  • Name and Lineage: Muḥammad ibn Ḥamzah al-Maghribī, attributed to his Moroccan origins. He was born in the 10th century AH (16th century CE).
  • Place and Date of Birth: Born in the Maghreb (Northwest Africa), in a scientific and culturally active environment.
  • Migration to the East: He later moved to Istanbul, where he settled at the Ottoman court, benefitting from the scientific patronage provided by the empire. In Istanbul, he devoted himself to study and authorship, becoming a major authority in arithmetic and algebra.

Social, Economic, and Political Environment

Ibn Hamzah was raised in a flourishing intellectual climate in the Maghreb, where institutions taught astronomy and mathematics, influenced by the legacies of al-Khwarizmi and Ibn Yunus.

Upon relocating to Istanbul, he encountered a highly developed scientific atmosphere supported by the Ottoman state, which actively encouraged scholarly production. The Sultan promoted research and writing, enabling Ibn Hamzah to expand his ideas and contributions in mathematics and algebra.

His Teachers and Their Influence

  • Scholars of the Maghreb: He was influenced by Ibn Yunus in astronomy and arithmetic, and drew from al-Khwarizmi’s foundational work in algebra and mathematics.
  • Scholars of the Ottoman Court:
  • Khwāja Zāda: A prominent Ottoman mathematician whose analytical methodology shaped Ibn Hamzah’s mathematical approach.
  • ʿAlī Qūshjī: An astronomer and mathematician who contributed to new geometric concepts from which Ibn Hamzah derived innovative methods for solving algebraic equations.

His Students and Later Influence

  • Ottoman Scholars: A number of students studied under him in the sultanic schools of Istanbul, where he taught algebra and geometry. Some of them advanced astronomical calculations and analytical geometry.
  • Indirect Influence: His works, once translated into Latin, inspired later European scientists and exposed them to his algebraic methodologies.

Major Scientific Contributions

  • Algebra: He developed new techniques for solving complex algebraic equations and introduced geometric concepts to simplify algebraic problems—contributing to the emergence of analytical geometry.
  • Simplification of Arithmetic: He devised shortcut methods for computing percentages, multiplication, and division, which impacted commerce and administration. He also compiled tables to simplify complex operations.
  • Applied Geometry: He contributed to precise geometric methods for calculating areas and lengths, which influenced Ottoman Islamic architecture.

His Works

  • Tuhfat al-Aʿdād fī al-Ḥisāb wa al-Jabr (The Gift of Numbers in Arithmetic and Algebra): His most important work, offering innovative solutions for algebraic equations and practical methods for simplifying calculations, with commercial applications.
  • Al-Kāfī fī al-Ḥisāb (The Sufficient in Arithmetic): Focuses on daily and commercial arithmetic, providing simplified approaches to complex operations.

Views of Muslim Scholars

  • Ibn Taghrī Birdī: “Ibn Hamzah was a creative mind in mathematics, masterfully uniting theory and application like no one before him.”
  • The Ottoman Historian Qāsim Afandī: “Ibn Hamzah’s writings stood out for their precision and scientific depth and became a point of reference for scholars in Istanbul and Greater Syria.”

Orientalist Views

  • Carl Brockelmann: “Ibn Hamzah was among the earliest to lay the foundation for modern algebra; his works influenced the European Renaissance.”
  • Edward Browne: “Ibn Hamzah’s writings marked a pivotal phase in the history of arithmetic and algebra, serving as foundational texts in Europe.”

Conclusion

Ibn Hamzah al-Maghribi stands as a towering figure in the history of Islamic mathematics. He pioneered novel methods in algebra and arithmetic, successfully integrating theoretical knowledge with practical applications. His contributions continue to resonate in modern educational curricula and serve as a call to revive the scientific legacy of Islamic civilisation and recognise its foundational role in the evolution of modern science.

References

  1. Ibn Hamzah al-Maghribi, Tuhfat al-Aʿdād fī al-Ḥisāb wa al-Jabr, ed. Muhammad Saʿid al-Kilani, Dar al-Kutub al-ʿIlmiyyah, Beirut, 2020.
  2. Carl Brockelmann, History of Arabic Literature, trans. Najib al-ʿAqiqi, Dar al-Fikr, Beirut, 1998.
  3. Edward Browne, A Literary History of Persia, Cambridge University, 1912.
  4. George Sarton, Introduction to the History of Science, Dar al-Maʿrifah, Beirut, 2003.
  5. ʿAbdullah ibn Saʿid, Scholars of the Maghreb and Their Impact on Islamic Sciences, Dar al-Fikr, Cairo, 2018.
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